Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  ios_base::sync_with_stdio(0);
  int n, n1, k1;
  cin >> n;
  n *= 2;
  int x = 0;
  for (int i = 1; i <= sqrt(n); i++) {
    n1 = n;
    n1 -= i * (i + 1);
    if (n1 <= 0) {
      break;
    }
    k1 = sqrt(n1);
    if (k1 * (k1 + 1) == n1) {
      x = 1;
      break;
    }
  }
  if (x == 1)
    cout << "YES";
  else
    cout << "NO";
}